An objective function for Hebbian self-stabilizing neural plasicity rules

ECHEVESTE, RODRIGO; GROS, CLAUDIUS

Congreso; DPG-Frühjahrstagung (German Physical Society Meeting) 2015, Condensed Matter Section; 2015

Objective functions provide a useful framework for the formulation ofguiding principles in dynamical systems. In the case of informationprocessing systems, such as neural networks, these guiding principlescan be formulated in terms of information theoretical measures with re-spect to the input and output probability distributions. In the presentwork, a guiding principle for neural plasticity is formulated in termsof an objective function defined as the Fisher information with respectto an operator that we denote as the synaptic flux[1]. By minimiza-tion of this objective function, we obtain synaptic plasticity rules thatboth account for Hebbian/anti-Hebbian learning and are self-limitingto avoid unbounded weight growth.As an application, the non-linear bars problem[2] is studied, in whicheach neuron is presented with a grid of inputs, depicting the superpo-sition of a random set of bars. We show that, under the here presentedrules, the neurons are able to learn single bars or points (the indepen-dent components of the input), even when these are never presentedin isolation.